BAIL 2006 Book of Abstracts - Institut für Numerische und ...

M.H. BUSCHMANN, M. GAD-EL-HAK: Turbulent Boundary Layers: Reality and
Myth
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International Conference on Boundary and Interior Layers—Computational & Asymptotic Methods
(BAIL 2006)
Abstract of keynote lecture for the
Minisymposium on Asymptotic Methods for Laminar and Turbulent Boundary Layers
Turbulent Boundary Layers: Reality and Myth
Matthias H. Buschmann
Privatdozent, Institut für Strömungsmechanik, Technische Universität Dresden, Dresden, Germany
Mohamed Gad-el-Hak
Caudill Professor and Chair of Mechanical Engineering,
Virginia Commonwealth University, Richmond, VA 23284-3015, USA
Hundred years after Ludwig Prandtl’s fundamental lecture on boundary layer theory, 1 the meanvelocity
profile and the shear-stress distribution of the seemingly simplest case of wall-bounded
flow, the zero-pressure-gradient turbulent boundary layer (ZPG TBL), still appears to be terra
incognita. Even less is known about confined and semi-confined flows undergoing pressure
gradients, such as pipe and channel flows and wall-bounded flows approaching pressure-driven
separation. The problem is of course related to the lack of analytical solutions to the
instantaneous, nonlinear Navier–Stokes equations that govern the stochastic dependent variables
of almost all turbulent flows. What little we know about turbulence comes from experiments and
heuristic modeling, not first-principles solutions. (Direct numerical simulations provide firstprinciples
integration of the instantaneous Navier–Stokes equations, but are at present limited to
modest Reynolds numbers and simple geometries.)
Consider a two-dimensional, isothermal, incompressible, steady flow over a body of length L.
The fluid may have constant density ρ and constant dynamic viscosity µ. Assuming that the
characteristic velocity is U, we write the Reynolds number as
Re= !UL µ (1)
It was Prandtl’s genius that discovered that, at sufficiently high Reynolds number, a thin shear
layer exists close to the body. The thickness of this layer δ is much smaller than L. Due to the
strong streamwise velocity gradient normal to the wall, even a small viscosity such as that for air
or water can cause considerable viscous shear stress, ! = µ "u "y . Originally Prandtl called this
layer therefore Reibungsschicht, which literally translates to friction layer.
Introducing the transformation
! ! ! ! ! $
( x,y
,u ,v , p ) ! & L x,Re
%
" 1
2 L y,U u,Re " 1
'
2 2
U v,#U p)
(
1 Prandtl, L., “Über Flüssigkeitsbewegung bei sehr kleiner Reibung,” Proc. Third Int. Math. Cong., pp. 484–491,
Heidelberg, Germany, 1904.
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M. H. Buschmann & M. Gad-el-Hak, Abstract for BAIL 2006
Speaker: BUSCHMANN, M.H. 32 BAIL 2006
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